POPL 2017
Sun 15 - Sat 21 January 2017
Wed 18 Jan 2017 16:30 - 16:55 at Amphitheater 44 - Logic Chair(s): Alexandra Silva

We extend the weak monadic second-order logic of one successor on finite strings (M2L-STR) to symbolic alphabets by allowing character predicates to range over decidable quantifier free theories instead of finite alphabets. We call this logic, which is able to describe sequences over complex and potentially infinite domains, symbolic M2L-STR (S-M2L-STR). We then present a decision procedure for S-M2L-STR based on a reduction to symbolic finite automata, a decidable extension of finite automata that allows transitions to carry predicates and can therefore model symbolic alphabets. The reduction constructs a symbolic automaton over an alphabet consisting of pairs of symbols where the first element of the pair is a symbol in the original formula’s alphabet, while the second element is a bit-vector. To handle this modified alphabet we show that the Cartesian product of two decidable Boolean algebras (e.g., the formula’s one and the bit-vector’s one) also forms a decidable Boolean algebras. To make the decision procedure practical, we propose two efficient representations of the Cartesian product of two Boolean algebras, one based on algebraic decision diagrams and one on a variant of Shannon expansions. Finally, we implement our decision procedure and evaluate the performance of our implementation on a comprehensive set of formulas.

Wed 18 Jan

Displayed time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change

16:30 - 17:45
LogicPOPL at Amphitheater 44
Chair(s): Alexandra Silva University College London
16:30
25m
Talk
Monadic second-order logic on finite sequences
POPL
Loris D'Antoni University of Wisconsin–Madison, Margus Veanes Microsoft Research
16:55
25m
Talk
On the Relationship Between Higher-Order Recursion Schemes and Higher-Order Fixpoint Logic
POPL
Naoki Kobayashi University of Tokyo, Japan, Etienne Lozes ENS Cachan, Florian Bruse University of Kassel
17:20
25m
Talk
Coming to Terms with Quantified Reasoning
POPL
Simon Robillard Chalmers University of Technology, Andrei Voronkov University of Manchester, Laura Kovacs Chalmers University of Technology